This study examines the optimality of stockless production in a manufacturing system subject to random disruptions. Based on a base-stock level policy, we explore conditions under which maintaining no inventories of end products minimizes total costs, including backordering penalties. Using a queueing model (M/Gamma/1) to represent production dynamics, we derive analytical expressions for key performance metrics. Our findings indicate that the feasibility of stockless production depends on process time, the importance of disruptions, demand, and cost structures. We further validate theoretical insights through numerical experiments, demonstrating how variability reduction and operational efficiency impact stockless strategies. This paper establishes analytical critical conditions for eliminating inventories.